##### Title: An Approximation of Fuzzy Numbers Based on Polynomial Form Fuzzy Numbers

##### Pages: 290-305

##### Cite as:

Sh. Yeganehmanesh, M. Amirfakhrian, An Approximation of Fuzzy Numbers Based on Polynomial Form Fuzzy Numbers, Int. J. Anal. Appl., 16 (2) (2018), 290-305.#### Abstract

In this paper, we approximate an arbitrary fuzzy number by a polynomial fuzzy number through minimizing the distance between them. Throughout this work, we used a distance that is a meter on the set of all fuzzy numbers with continuous left and right spread functions. To support our claims analytically, we have proven some theorems and given supplementary corollaries.

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#### References

- S. Abbasbandy, M. Amirfakhrian, The nearest trapezoidal form of a generalized left right fuzzy number, Int. J. Approx. Reason. 43 (2006), 166-178.
- S. Abbasbandy, B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity, Appl. Math. Comput. 156 (2004), 381-386.
- M. Amirfakhrian, Numerical Solution of a System of Polynomial Parametric form Fuzzy Linear Equations, Book Chapter of Ferroelectrics, INTECH Publisher, Austria, (2010).
- A. I. Ban, L. Coroianu, Existence, uniqueness and continuity of trapezoidal approximations of fuzzy numbers under a general condition, Fuzzy Sets Syst. 3 (2014) 3-22.
- D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Application, Academic Press, New York, (1980).
- L. Coroianu, M. Gagolewski, P. Grzegorzewski, Nearest piecewise linear approximation of fuzzy numbers, Fuzzy Sets Syst. 233 (2013), 26-51.
- P. Grzegorzewski, Metrics and orders in space of fuzzy numbers, Fuzzy Sets Syst. 97 (1998), 83-94.
- P. Grzegorzewski, Nearest interval approximation of a fuzzy number, Fuzzy Sets Syst. 130 (2002), 321-330.
- P. Grzegorzewski, P. Mró wka, Trapezoidal approximations of fuzzy numbers, Fuzzy Sets Syst. 153 (2005), 115-135.
- P. Grzegorzewski, K. Pasternak-Winiarska,Natural trapezoidal approximations of fuzzy numbers, Fuzzy Sets Syst. 250 (2014), 90-109.
- M. Ma and A. Kandel and M. Friedman, Correction to ”A new approach for defuzzification”, Fuzzy Sets Syst. 128 (2002), 133-134.
- V. Powers, B. Reznick, Polynomials that are positive on an interval, Trans. Amer. Math. Soc. 352 (10) (2000), 4677C4692.
- J. Stolfi, M.V.A. Andrade, J.L.D. Comba, and R.Van Iwaarden. Affine arithmetic: a correlation-sensitive variant of interval arithmetic, accessed January 17, (2008).
- W. Voxman, Some remarks on distance between fuzzy numbers, Fuzzy Sets Syst. 100 (1998), 353-365.
- H. J. Zimmermann, Fuzzy Set Theory and Its Applications, 2 nd Edition, Kluwer Academic, Boston, (1991).